Flexural analysis of 3-legged tower

[bjcure]

I've got a 3-legged trussed tower composed of three pipe columns in each corner. In plan view it is an equilateral triangle. Between the pipe columns are vertical and diagonal web members. If I apply a moment to the tower, about an axis that parallels two of the legs, how do I calculate the tension and compression? Does one column take all the compression and the other two columns take the tension (or vice versa if the moment is in the opposite direction)? In other words, would one column have double the axial load as the two other columns (except opposite direction)? Or is it more complicated than that?

 

[hokie66]

If the load is perpendicular to one side, it is as you described it. But if the load is parallel to one side, the truss on that side takes all the load. So equal tension and compression in two columns. The third column is at the neutral axis, so no load. In that situation, the third leg and the lacing just provide lateral support. Whichever way you look at it, all three legs have to be designed for the same force.

 

[rscassar]

That's how I see it. World famous engineers have taken this "Y" configuration and made very tall buildings from it.

http://en.wikipedia.org/wiki/Burj_Khalifa

 

[paddingtongreen]

Without disagreeing, if you run this through an FEM program with fixed joints (reasonable for a pipe structure) you will get bending in the bracing members and torsion on the center leg when the wind is parallel to one face, because of the deflection of the wind resisting frame.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[hokie66]

Michael, old friend, I disagree with using fixed joints. Why would you do that? Besides, we don't even know what type members the webs are.

 

[paddingtongreen]

I didn't say that correctly, there will be bending in all of the web members and torsion in all of the columns.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[rb1957]

each leg would react a portion of the applied moment ...

each leg will be in bending (with pinned reactions), the load in each leg will not be axial (which was my 1st guess)

there'll be a set of vertical couples (on the obvious two legs) and a set of lateral couples on all three legs.

not a trival problem !? made more complicated if there are fixed ends to the legs.

 

[paddingtongreen]

hokie66, LOL, I assumed the web members would be round HSS. Even with pinned joints, I think there is a torsion resulting when the wind is parallel to the one face.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[bjcure]

Thanks for the commments everyone. FYI, it's a small tower and the legs are only 16" apart from centerline to centerline of each column. The 3 pipe columns are 1.25" outside diameter. The web members are 7/16" diameter solid round bars.

I'm mainly trying to confirm that the column axial tension/compression loads can be taken from the moment divided by "d". In this case, "d" would be (16")x(sq. root of 3)/2 = 13.85". A colleague felt that I should divide the moment by the distance to the neutral axis, or find the "I" of the entire configuration of columns and do an extreme fiber stress analysis. That doesn't seem appropriate to me in this case, but it did make me question it.

 

[rb1957]

IMHO, that's probably alittle simplistic. I'd draw a FBD of a leg, assume the applied moment is carried by the two (obvious) legs. I suspect that the reaction to the ground could be a simple couple (which is not axial load in the legs).

btw, if "the legs are only 16" apart from centerline to centerline of each column", why wouldn't you use this as the moment arm for the couple, instead of "(16")x(sq. root of 3)/2" ?

not sure how the web members would affect the solution, obviously they provide an opportunity for load transfer between the legs. i think a quick FEM would provide insight and a better answer than a mass of assumptions.

 

[BAretired]

If the tower carries significant gravity load, such as an elevated water tank, the legs can buckle in a torsional mode.

BA

 

[Ron]

Ah...another argument ensues about pinned or fixed connections in a welded truss or space frame!

To check column buckling with wind perp. to a flat face, use pinned connections. To check interaction and torsion, use fixed connections or orthogonal springs to model some fixity (probably too much effort for such a small frame).

If you are hand-calculating this, the critical case will be with two columns in tension and one in compression, using your approach without considering extreme fiber stress.

I'm assuming this is a small antenna tower, likely less than 50 feet high.

 

[bjcure]

rb1957,

The center-to-center distance at the perimeter of the triangle is 16" between the columns. The distance from the midpoint between two columns to the third column is 13.85". I'll run this (or something like it) through an FEA at some point and see what happens. Just curious what you mean by a couple not being axial loads in the legs. Isn't the definition of a couple two axial loads acting in opposite directions separated by a certain distance?

Ron,

What you said made sense. I was just checking column buckling. It's a 120 foot tower supporting a small wind turbine, but is guyed near the top and at the 1/3 points.

 

[rb1957]

i had pictured the moment applied so that one leg was under the moment axis, therefore unloaded, and the moment was reacted by the other two legs.

instead the moment is applied so that one leg reacts one of the couple loads and the other load is reacted by two legs. then 13.85" is the right couple arm. the reactions are vertical, not inclined along the leg.

i suggest you draw a FBD of a legs ... the one leg normal to the plane of bending (reacting P = M/d) is straight forward (i think !?) but the inclined legs are seeing some less obvious secondary effects (i think).

 

[hokie66]

Guyed towers such as you described are often used for communication towers. It is also true that they are notorious for collapsing. Be sure to leave plenty of clear space around the tower.

 

[rscassar]

I believe the critical case is the one I sketched where 1 leg is in tension, 1 leg is in compression and the other leg doesn't seen any force because it is located at the neutral axis.

I agree with your colleague suggesting that you calculate I values to calculate reaction forces.

I would neglect the stiffness increased by the web members.

This is a spreadsheet I worked on for bolt groups but it can be used to calculate reactions.

 

[hokie66]

kikflip,
How can that be the critical case? The loading is less and the lever arm is greater.

Calculate I and use Mc/I, or just use M/d, you get the same result.

 

[paddingtongreen]

The guys change everything. It takes the problem out of the engineering realm into that of the black arts.

As I look at it, the wind on the structure's leading leg is the worst case, all of the horizontal load is resisted by one set of guys and all of the vertical component from those guys goes into that lead column. The other guys are slack since the tower tends to move towards them.

All of this, without considering ice and temperature differences. Definitely black art territory.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[hokie66]

Frustrating, isn't it, Michael? It took 13 posts before we found out this was a guyed mast.

 

[paddingtongreen]

Hokie, I almost shouted "The guys change everything." in bold, upper case.

Michael.
Timing has a lot to do with the outcome of a rain dance.